Cremona's table of elliptic curves

585 = 3² · 5 · 13

Field	Data	Notes
Atkin-Lehner	3- 5+ 13-	Signs for the Atkin-Lehner involutions
Class	585g	Isogeny class
Conductor	585	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	-142155 = -1 · 37 · 5 · 13	Discriminant
Eigenvalues	-2 3- 5+ -3  5 13- -5  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-3,18]	[a1,a2,a3,a4,a6]
Generators	[-1:4:1]	Generators of the group modulo torsion
j	-4096/195	j-invariant
L	1.0788350162505	L(r)(E,1)/r!
Ω	2.7101707230781	Real period
R	0.099517256151417	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	9360bp1 37440ci1 195b1 2925h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 585g1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-2	-	+	-3	5	-	-5	2	1	-10	-2	-3	9	-4	-10	-9	0	-11	-4	-15	6	-11	-8	11	-9

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Quadratic twists for elliptic curve 585g1

-4	8	-3	5	-7	-11	13
9360bp1	37440ci1	195b1	2925h1	28665bu1	70785q1	7605r1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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